If $y = f(x) = \frac{x + 2}{x - 1}$,then $x = $

If $f(x) = \int\limits_0^x {\frac{1}{{\sqrt {1 + {t^3}} }}\,} dt$ and $h(x)$ is the inverse of $f(x)$,then the value of $\frac{{h''(x)}}{{{h^2}(x)}}$ is

If $g(x)$ is the inverse function of $f(x)$ and $f^{\prime}(x) = \frac{1}{1+x^4}$,then $g^{\prime}(x)$ is

Let $f: W \rightarrow W$ be defined as $f(n) = n-1$ if $n$ is odd and $f(n) = n+1$ if $n$ is even. Show that $f$ is invertible. Find the inverse of $f$. Here,$W$ is the set of all whole numbers.

Consider the function $f = \{(1,2), (2,1), (3,1)\}$. Is $f$ invertible?

If the function $f(x) = x^3 + e^{x/2}$ and $g(x) = f^{-1}(x)$,then the value of $g^{\prime}(1)$ is